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Isodiametric and Isoperimetric Inequalities for Complexes and Groups
Author(s) -
Papasoglu P.
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700008942
Subject(s) - isoperimetric inequality , bounding overwatch , mathematics , context (archaeology) , group (periodic table) , function (biology) , bounded function , combinatorics , pure mathematics , exponential function , isoperimetric dimension , distortion (music) , mathematical analysis , computer science , physics , paleontology , amplifier , computer network , bandwidth (computing) , quantum mechanics , artificial intelligence , evolutionary biology , biology
It is shown that D. Cohen's inequality bounding the isoperimetric function of a group by the double exponential of its isodiametric function is valid in the more general context of locally finite simply connected complexes. It is shown that in this context this bound is ‘best possible’. Also studied are second‐dimensional isoperimetric functions for groups and complexes. It is shown that the second‐dimensional isoperimetric function of a group is bounded by a recursive function. By a similar argument it is shown that the area distortion of a finitely presented subgroup of a finitely presented group is recursive. Cohen's inequality is extended to second‐dimensional isoperimetric and isodiametric functions of 2‐connected simplicial complexes.